Some of Donald Trump’s supporters watched with trepidation as he was whisked around Washington last week to powwow with GOP leaders and markedly softened his tone, worried that he was being co-opted by the party establishment.

Mr. Trump became the presumptive Republican presidential nominee because voters were thrilled by his outsider campaign that bashed the establishment, insulted rivals and defied political correctness with get-tough policies such as temporarily banning Muslims from entering the United States.

But after locking up the nomination, the real estate mogul goes to Washington and cozies up to House Speaker Paul D. Ryan, makes nice campaign rival Sen. Lindsay Graham and says his big plans are mere “suggestions.”

He vowed that the grass-roots movement ignited by Mr. Trump wouldn’t stand for backsliding by the real estate mogul under the guise of unifying the party.

“We’ve got to step up our game and make sure he stays true to his outsider roots and remains true to what he said in the primary season and that was turn Washington upside down and not be part of the political class,” said Mr. Kreitz.

“He’s going to get back to his roots or those of us who support him will demand that he gets back to his roots — or it’s going to get ugly this fall,” he said.

The movement behind Mr. Trump doesn’t want him to make concessions to GOP establishment figures such as Mr. Ryan, a Wisconsin Republican who is detested by hard-core conservatives for failing to fight President Obama’s deportation amnesty, Obamacare or plans to accept thousands of Syrian refugees.

“Most tea party people feel that Paul Ryan is part of the establishment so they are not going to put a lot of stock in having him endorse anybody,” said Reagan G. George, a tea party activist in Northern Virginia.

In the primary, he supported Sen. Ted Cruz of Texas, but he said he fully backed Mr. Trump as the likely nominee. Mr. George warned that every Republican candidate risked being co-opted because they must “deal with the spineless Republicans we’ve got in the House and in the Senate.”

Mr. George said it was similar to the agenda that Mr. Ryan espoused, although he didn’t think Mr. Ryan’s deeds matched his words.

Still, Mr. Ryan’s hesitancy to support the presumptive nominee angered Mr. Trump’s supporters as much as the billionaire businessman’s willingness to woo support from the speaker.

“It’s his job as a leader in the Republican Party to reach out to the nominee,” said Jeff Moorman, a conservative activist who volunteered for the Trump campaign in Iowa.

He said Mr. Trump had to “play politics a little bit” to get the party establishment behind him. But he warned Mr. Trump not to let party leaders mold the agenda, such as backing off on thr border wal.